Derivatives worksheet with answers

Free printable Derivatives worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xyx = −2

Let f(x) = −2x4 − 6x2 + 7x + 1. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −2x4 − 6x2 + 7x + 1x = −2
f′(−2) =
2.Easy
xyx = 1

Let f(x) = −4x4 − 6x2 + 5x + 9. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x4 − 6x2 + 5x + 9x = 1
f′(1) =
3.Medium
xyx = 2

Let f(x) = (−2x + 1)4. Find f′(2).

f(x) = (−2x + 1)4x = 2
f′(2) =
4.Medium
xyx = 1.5

Let f(x) = x·sin(3x), with x in radians. Find f′(1.5).

f(x) = x·sin(3x)x = 1.5 rad
f′(1.5) =
5.Hard
xyx = 3

The tangent line to f(x) = 3x2 − 2x + 3 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 3x2 − 2x + 3x = 3
b =
6.Hard
xyx = −2

The tangent line to f(x) = 0.5x2 + 3 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 3x = −2
b =

Answer key

  1. 1. f′(−2) = 95
  2. 2. f′(1) = −23
  3. 3. f′(2) = 216
  4. 4. f′(1.5) = −1.926
  5. 5. b = −24
  6. 6. b = 1

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